Performs the Wallraff test of angular distances or angular dispersion around the mean.
Arguments
- samples
list of samples of orientations
- ref
a vector of angles (in degrees) used as reference to compute the angular distances from, in each group. It should contain either one element (a common reference for all groups) or as many elements as there are groups, in the same order as the elements of the list
samples.If
refisNULL(the default), the mean angle of each group will be used as reference. In this situation, the Wallraff test becomes a comparison of angular dispersion around the mean- axial
logical. Whether the data are axial, i.e. \(\pi\)-periodical (
TRUE, the default) or directional, i.e. \(2 \pi\)-periodical (FALSE). In case of axial data, the angles will be doubled for the test.
Value
A list with class "htest" containing the following components:
- statistic
the chi-squared statistic from
kruskal.test.- parameter
the degrees of freedom for the chi-squared statistic.
- p.value
the p-value for the test.
- method
a character string containing the name of the test.
- data.name
a character string giving the name(s) of the data.
Details
The Wallraff test of angular distances between two or more groups is performed and the results are printed. The null hypothesis is that distances are equal across groups.
The test proceeds by computing the angular distances from a reference angle, in each group. The angular distance between two angles is the circular range. Then the distances are compared with a usual rank sum test (Kruskal-Wallis, stats::kruskal.test). When there are only two groups, the Wilcoxon-Mann-Whitney test could be used but stats::wilcox.test without continuity correction for the p-value is equivalent to stats::kruskal.test so only stats::kruskal.test is used here.
The Wallraff test is most frequently used to compare angular dispersion around the mean, between samples. In this case, the reference angle is the mean angle of each sample. This is the default here, when no reference angles are provided.
References
Batschelet, E (1981). Circular Statistics in Biology. chap. 6.10, p. 124
Zar, J H (2010). Biostatistical analysis. sec. 27.7-8, p. 643
See also
Other Two-Sample-Tests:
ar_test(),
equal_kappa_test(),
uniform_scores_test(),
watson_two_sample,
watson_wheeler_test_perm(),
watson_williams_test()
Examples
set.seed(20250411)
x1 <- c(35, 45, 50, 55, 60, 70, 85, 95, 105, 120)
x2 <- c(75, 80, 90, 100, 110, 130, 135, 140, 150, 160, 165)
walraff_test(list(x1, x2))
#>
#> Wallraff rank sum test of angular distance to the sample mean
#> directions
#>
#> data: 1 and 2
#> Kruskal-Wallis chi-squared = 0.40165, df = 1, p-value = 0.5262
#>
x1 <- rvm(100, mean = 90, kappa = 20)
x2 <- rvm(100, mean = 90, kappa = 10)
x3 <- rvm(100, mean = 90, kappa = 1)
walraff_test(list(x1, x2, x3))
#>
#> Wallraff rank sum test of angular distance to the sample mean
#> directions
#>
#> data: 1 and 2 and 3
#> Kruskal-Wallis chi-squared = 116.51, df = 2, p-value < 2.2e-16
#>
# San Andreas Fault Data:
data(san_andreas)
data("nuvel1")
PoR <- subset(nuvel1, nuvel1$plate.rot == "na")
sa.por <- PoR_shmax(san_andreas, PoR, "right")
walraff_test(list(sa.por$azi.PoR, rvm(100, 135, 10)))
#>
#> Wallraff rank sum test of angular distance to the sample mean
#> directions
#>
#> data: 1 and 2
#> Kruskal-Wallis chi-squared = 0.082398, df = 1, p-value = 0.7741
#>